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A figurate number of the form P_n^((4))=1/6n(n+1)(2n+1), (1) corresponding to a configuration of points which form a square pyramid, is called a square pyramidal number (or ...

The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...

A binary unit of information equal to 8 bits. Unfortunately, the storage of binary numbers in computers is not entirely standardized. Because computers store information in ...

Let {a_i}_(i=1)^n be a set of positive numbers. Then sum_(i=1)^n(a_1a_2...a_i)^(1/i)<=esum_(i=1)^na_i (which is given incorrectly in Gradshteyn and Ryzhik 2000). Here, the ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

Given a Poisson distribution with rate of change lambda, the distribution of waiting times between successive changes (with k=0) is D(x) = P(X<=x) (1) = 1-P(X>x) (2) = ...

A minimal surface and double algebraic surface of 15th order and fifth class which can be given by parametric equations x(u,v) = 2sinhucosv-2/3sinh(3u)cos(3v) (1) y(u,v) = ...

The lemniscate functions arise in rectifying the arc length of the lemniscate. The lemniscate functions were first studied by Jakob Bernoulli and Giulio Fagnano. A historical ...

The negative binomial distribution, also known as the Pascal distribution or Pólya distribution, gives the probability of r-1 successes and x failures in x+r-1 trials, and ...

A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid. For a right pyramidal frustum, let s be the slant height, h the ...